Suppose $U_{n}^{}:[a,b]\to \mathbb{R}$ is continuous. Suppose also that $U_{n}$ uniformly converges to $l(x)$.
I know that the following definition hold:
$$\forall\epsilon>0,\exists N:\forall n>N,\forall x \in [a,b]:|U_{n}(x)-l(x)|<\epsilon.$$
But my book uses this one:
$$\forall\epsilon>0,\exists N:\forall n>N,\forall x \in [a,b]:|l(x)-U_{n}(x)|<\frac{\epsilon}{b-a}.$$
Where does this come from? Thanks